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Effective matrix formalism for singularity analysis of differential equations and new intergrable system in nonlinear elasticity
Author(s) -
Novozhilova L.S.,
Urazhdin S.V.
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700305
Subject(s) - nonlinear system , singularity , laurent series , formalism (music) , elasticity (physics) , nonlinear elasticity , ode , mathematics , matrix similarity , taylor series , differential equation , mathematical analysis , mathematical physics , partial differential equation , physics , quantum mechanics , art , musical , visual arts , thermodynamics
We introduce a simple matrix formalism for Taylor series and generalized Laurent series that can be used for implementing the Taylor method for nonlinear ODEs and singularity analysis of differential equations. Advantages of this approach over conventional techniques are shown on model examples. Surprisingly, the same formalism can be used for proving C‐integrability of a 3D model in nonlinear elasticity. An alternative proof is obtained by using similarity between the model in nonlinear elasticity and the classic Pohlmeier‐Lund‐Regge model from high energy physics. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)